Question

find the values of the unknowns in each of the following rhombuses
pls help me :))​

Answer 1

Answer:

q = 74°

step by step explanation

for figure ( a)

ABD = ADB ( angle opposite to equal opposite sides are equal )

ABD = 38°

ABD + ADB + q = 180° ( angle sum property of triangle )

38+38 + q = 180°

106 + q = 180

q = 180 - 106

q = 74°

Answer 2

Given:- For part (1)-

ABCD is a rhombus

 ∠BDA = 38°

For part (2)-

DCBA is a rhombus

∠BAC = 42°

To find:- For part (1)-

value of ∠q and ∠p

For part (2)-

value of ∠r and ∠s

Solution:-

For part (1)-

∠BDA = ∠p                                         (alternate angles)

∴ ∠p = 38°

So, ∠DBA = 90° - 38°                        ( in a rhombus every angle is 90°)

∠DBA = 52°

Now, in ΔADB,

∠DBA + ∠q + ∠BDA = 180°                (angle sum property of a triangle)

52° + ∠q + 38° = 180°

∠q + 90° = 180°

∴ ∠q = 90°

For part (2):-

∠BAC = 42°                                                 (given)

∠BAC = ∠r                                  (alternate angles)

∴ ∠r = 42°

Now, ∠CAD = 90° - ∠BAC           (in rhombus every angle is of 90°)

so, ∠CAD = 48°                             (a)

Now, in ΔDEA,

∠AED = 90°                  (diagonals of a rhombus intersect each other at 90°)

∠EAD = 48°                                    (because of a)

S0,

∠AED + ∠s + ∠EAD = 180°            (angle sum property)

90° + ∠s + 48° = 180°

∠s = 42°

Hence, the values of the unknown values are answered.

#SPJ2